We present a model predictive control algorithm for cooperative trajectory planning of robot manipulators subject to collision avoidance in a shared confined environment. To this end, we propose the approximation of the geometry of the robots by smooth Bézier curves and spherical objects. Addition-ally, we introduce velocity constraints for collision avoidance, enforcing such robot geometry approximations to slide along tangential planes defined by two collision spheres placed at the corresponding nearest points of the two robots. These velocity constraints are embedded into a centralized model predictive control algorithm for the computation of minimum-time trajectories for two cooperative robot manipulators. The performance of the proposed control scheme is demonstrated by simulations of highly critical coordinated synchronous pick-and-place robot task executions.